Damped & Forced Oscillations
Q. What type of damping is characterized by the system oscillating with gradually decreasing amplitude?
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A.
Underdamping
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B.
Critical damping
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C.
Overdamping
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D.
No damping
Solution
Underdamping is characterized by oscillations with gradually decreasing amplitude.
Correct Answer: A — Underdamping
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Q. What type of damping occurs when the damping force is proportional to the velocity of the oscillator?
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A.
Critical damping
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B.
Underdamping
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C.
Overdamping
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D.
Linear damping
Solution
Linear damping occurs when the damping force is directly proportional to the velocity of the oscillator.
Correct Answer: D — Linear damping
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Q. What type of damping occurs when the damping ratio is greater than 1?
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A.
Underdamped
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B.
Critically damped
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C.
Overdamped
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D.
Free oscillation
Solution
When the damping ratio is greater than 1, the system is overdamped and returns to equilibrium without oscillating.
Correct Answer: C — Overdamped
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Q. Which of the following describes overdamped oscillations?
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A.
System oscillates with decreasing amplitude
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B.
System returns to equilibrium without oscillating
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C.
System oscillates indefinitely
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D.
System oscillates with constant amplitude
Solution
In overdamped oscillations, the system returns to equilibrium without oscillating due to strong damping.
Correct Answer: B — System returns to equilibrium without oscillating
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Q. Which of the following describes the motion of a damped oscillator mathematically?
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A.
x(t) = A cos(ωt)
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B.
x(t) = A e^(-bt) cos(ωt)
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C.
x(t) = A sin(ωt)
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D.
x(t) = A e^(bt) cos(ωt)
Solution
The motion of a damped oscillator is described by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.
Correct Answer: B — x(t) = A e^(-bt) cos(ωt)
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Q. Which of the following describes the motion of a damped oscillator?
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A.
Simple harmonic motion
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B.
Exponential decay
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C.
Linear motion
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D.
Circular motion
Solution
The motion of a damped oscillator is characterized by exponential decay of amplitude over time.
Correct Answer: B — Exponential decay
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Q. Which of the following describes the motion of a system undergoing overdamping?
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A.
Returns to equilibrium position quickly
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B.
Oscillates with decreasing amplitude
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C.
Returns to equilibrium position slowly without oscillating
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D.
Oscillates indefinitely
Solution
In overdamping, the system returns to the equilibrium position slowly without oscillating.
Correct Answer: C — Returns to equilibrium position slowly without oscillating
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Q. Which of the following is a characteristic of overdamped systems?
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A.
They oscillate slowly
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B.
They return to equilibrium slowly without oscillating
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C.
They oscillate rapidly
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D.
They have maximum amplitude
Solution
Overdamped systems return to equilibrium slowly without oscillating, as the damping is strong.
Correct Answer: B — They return to equilibrium slowly without oscillating
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Q. Which of the following is a characteristic of underdamped oscillations?
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A.
No oscillation occurs
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B.
Oscillations decay slowly
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C.
Oscillations decay rapidly
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D.
Oscillations are constant
Solution
Underdamped oscillations occur when the damping is weak, allowing the system to oscillate with a gradually decreasing amplitude.
Correct Answer: B — Oscillations decay slowly
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Q. Which type of damping results in the system returning to equilibrium without oscillating?
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A.
Underdamping
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B.
Critical damping
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C.
Overdamping
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D.
No damping
Solution
Critical damping allows the system to return to equilibrium in the shortest time without oscillating.
Correct Answer: B — Critical damping
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